AL Solids P.23

Types of solids Crystalline (Long range order) e.g. metals, sugar, salt

P.23 Types of solids Amorphous (Disorder) e.g. glass

P.23 Crystal structures Kinds of bonds formed - Hydrogen bond - Ionic bond - Covalent bond - Metallic bond Size and shape - fcc - bcc

P.24 Size of a molecule Monolayer experiment

P.24 Size of a molecule Using Avogadro constant

P.25 Elasticity of metals

P.25 Hooke’s Law The extension is proportional to the force in a wire if the proportional limit is NOT exceeded.

P.25 Stress and Strain Strength The Greatest force a material can withstand before breaking Stiffness (force constant) The opposition a material sets up to being distorted by having its change of size and/or shape. Stress The force acting on unit cross-sectional area Stress = F / A Strain The extension of unit length Strain = e / l

P.26 Stress S=(Weight W) / (Area A) New volume V’ = 2 3 V = 8V New weight W’ =  V’ g = 8  V g = 8 W New area A’ = 2 2 A = 4 A New Stress S’ = (8 W) / (4 A) = 2 S

P.27 Stress and strain behaviour of ductile material

P.27 Stress and strain behaviour of ductile material

P.27 Ductile materials Lengthen and undergo plastic deformation until they break

P.27 Brittle materials Lengthen and break just after elastic limit L is reached.

P.28 Fatigue Under varying stress, fracture may occur even the maximum stress has not reached.

P.28 Creep Under high temperature, the metal continues to deform even under constant stress.

P.28 Young’s modulus E Under elastic limit, stress α strain

P.29 Experiment

P.26 mg = ke E = (F l) / (A e) F = [(E A) / (l)] e k = [(E A) / (l)] For same material, Young modulus will be the same New l’ => new k’=2k m’g = k’e’ + k’e’ 2m g = 2ke’ + 2ke’ e’ = (0.5) e

P.30 Q: larger strain before break P: E=stress/strain = slope = stiffness strength = greater breaking stress

P.31  =  /E. Strain is independent of the unstretched length N N Y  =  /E =(F/(EA)). When A increases,  decreases.  =  /E =(F/(EA)). E brass < E steel. When E decreases,  increases.

P.31 %E = %m + %g + %l + 2%d + %e %l = 0.51% %d = 1.64% %m = 0.1% %e = 2.56% %g = 1.02%

P.31 Energy stored in a wire

P.32 Energy per unit volume of a wire

P.32 Energy on the wire

P.32 Energy on the wire

P.32

l’  mg

P.32 Their extensions should be the same. x Taking moment at point O O

P.33 These two wires are connected in series. They have same force.

P.33 mg = k x Y Y N m  x x = mg / kx depends on weight of the ball and force constant k The ball eventually stopped, energy is lost due to air resistance.

P.33

P.34

P.35

P.36

P.38 Stress – strain curves for glass, copper and rubber

P.38 Stiffer material needs a greater stress to produce same strain. Young modulus is larger which has steeper slope. Y Y Y Stronger material can withstand a greater stress before breaking Z breaks at strain=1.6, hence e = 1.6l. The length of Z at breaking point = 2.6 l

P.38 Ductility is independent of its melting point. Young modulus is a measure of stiffness. It is NOT a direct measurement of the ductility of material. Copper has performed plastic deformation between the elastic limit and the facture point. Glass has narrow gap only. Extension under same stress depends on the proportional part. It is independent of plastic deformation.

P.39 Intermolecular forces

P.40 Equilibrium spacing of molecules Stable equilibrium occurs when P.E. is minimum.

P.40 Elasticity and Hooke’s Law Near r o, F-r curve is nearly a straight line

P.40 Thermal expansion At higher temperature, molecules have some energy and oscillate between X and Y. Due to asymmetry, mean position will be G. Metal is expanded. At very high temperature, the molecule separation will be very large. The corresponding energy needed is called latent heat or binding energy.

P.41

(1) : Spacing of molecules at equilibrium (2) : Max. distance before breaking (3) : force constant => stiffness (4) : max. tension that the material can tolerate before breaking, it is called tensile strength.

P.42 U=0

P.42

A 1 is +ve energy that the system repel back to eq. pt. A 2 is -ve energy that the system attract back to eq. pt. with max. attractive force. A 3 is -ve energy that the material breaks and go to infinity A 2 + A 3 is energy needed to move the molecules from eq. pt to infinity

P.43